Hello Maddie,

The Kruskal-Wallis is a one-way anova counterpart, which doesn't require interval-strength data or normality of model residuals. It does, though, require homogeneity of variance across groups.

From your description, your design includes three factors (pheromone, virgin/mated, and treated/control). As well, you noted that none of the control condition cases responded, so it sounds as if you could exclude that factor altogether (treated/control), use only treated (non-control) cases in the main analysis and note the outcome in your write-up.

So, two factors remain for analysis: pheromone and virgin/mated. You could: (a) run a K-Wallis on the four groupings; then (b) follow-up with individual K-Wallis or Mann-Whitney tests on individual pairs if a difference is detected in the first step.

Alternatively, you could use exact/permutation or bootstrap/resampling approaches to a two-way anova, which allows avoidance of concern over normality and homogeneity.

Here are some resources that you may find helpful:

1. https://statweb.stanford.edu/~tibs/stat315a/Supplements/bootstrap.pdf

2. https://machinelearningmastery.com/a-gentle-introduction-to-the-bootstrap-method/

3, https://www.burns-stat.com/documents/tutorials/the-statistical-bootstrap-and-other-resampling-methods-2/

Good luck with your work.

There is the Scheirer–Ray–Hare test. A non-parametric analogous to Two-Way ANOVA (A two-way KW test, for convenience).

Dear Maddie,

David is right: Kruskal-Wallis and U-Mann-Whitney tests could be used. What sort of software will you use?

Best,

Guy